The uniqueness of the strongly regular graph on 77 points
β Scribed by A. E. Brouwer
- Publisher
- John Wiley and Sons
- Year
- 1983
- Tongue
- English
- Weight
- 329 KB
- Volume
- 7
- Category
- Article
- ISSN
- 0364-9024
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π SIMILAR VOLUMES
Let G be a 2-connected d-regular graph on n rd (r 3) vertices and c(G) denote the circumference of G. Bondy conjectured that c(G) 2nΓ(r&1) if n is large enough. In this paper, we show that c(G) 2nΓ(r&1)+2(r&3)Γ(r&1) for any integer r 3. In particular, G is hamiltonian if r=3. This generalizes a resu
## Abstract It was only recently shown by Shi and Wormald, using the differential equation method to analyze an appropriate algorithm, that a random 5βregular graph asymptotically almost surely has chromatic number at most 4. Here, we show that the chromatic number of a random 5βregular graph is as
Let G be a regular graph of girth n( 2 5 ) and valency k ( r 3 ) , that has the least possible number f(k, n ) of vertices. Although the existence of such a graph was proved by Erdos and Sachs (see Ref. 6, p. 82), only a few cases have been solved (see Refs. 2-7). Recently, O'Keefe and Wong have sho